Perfectly reflective surfaces

I was thinking, If somehow we could create a perfectly reflective surface, create a sphere with it, couldnt we technically trap LIGHT inside of it? If a surface was perfectly reflective could it still be used as a solar sail since all the energy of the light is left completely the same after it is reflected?

I just got out of highschool so I really have no idea of the theories or anything behind this, so could someone with more knowlege explain if this is possible?

First off, note that talking about things that can't happen in physics (perfect reflectivity) is kinda like talking about a square triangle.  Since you start with a false premise, it's likely you'll end up with impossible conclusions.

Let us suppose I have a perfectly reflective sphere sitting here on my desk.  Furthermore, let us suppose that I insert a ray of light into the sphere, heading east.  The ray will hit the east wall of the sphere, and bounce back.

In order for momentum and energy to be conserved, two things will need to have happened.  First, the ball must have started to roll a little bit to the east.  Second, the "speed" of the photon (it's frequency in terms of wave theory) will need to have decreased.  Because the mass of the sphere is much much more than the "mass" of the photon, this is hardly noticable.

Still, this reflection wasn't a perfect one, because the wave has made a very minute red shift, but at least it conserved as much as physically possible.

So now this sphere is microscopically rolling eastward on my desk.  Assuming that it loses no velocity, then when the light ray bounces to hit the western wall of the sphere, the process will be reversed, and the sphere will remain stationary again untill the light returns to hit the east side of the sphere again, restarting the process.  The sphere will move in small eastward jerks while the ray inside goes from low energy to high energy.

Now, I have assumed that the interior of the sphere is a perfect vacuum.  I cannot really make the same assumption about the outside of the sphere.  It is on my desk, as it rolls eastward, it will bounce off with air particles and forces, which tend to turn it's kinetic energy into heat.  This is entropy in action.

Since the sphere has lost kinetic energy, the ray must red shift again in order to maintain momentum and energy conservation on the western bounce.

So if we take into account the fact that whatever the light propels will be affected by some sort of entropy, the light itself will lose energy and frequency with every bounce.  Eventually, it's just going to become a radio wave and fly out of the sphere.

So... as long as we're operating in a universe where this reflective surface is under the effect of forces that will convert it's kinetic energy to heat, you can't trap light inside a 'perfectly' reflective surface.

Furthermore, ignoring entropy, if light reflects off of any 'perfectly' reflective surface of non-infinite mass, the light will undergo a very small red shift in order to conserve momentum/energy.